Problem: Simplify the following expression: $ a = \dfrac{-5}{3} - \dfrac{k - 3}{k - 4} $
Solution: In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{k - 4}{k - 4}$ $ \dfrac{-5}{3} \times \dfrac{k - 4}{k - 4} = \dfrac{-5k + 20}{3k - 12} $ Multiply the second expression by $\dfrac{3}{3}$ $ \dfrac{k - 3}{k - 4} \times \dfrac{3}{3} = \dfrac{3k - 9}{3k - 12} $ Therefore $ a = \dfrac{-5k + 20}{3k - 12} - \dfrac{3k - 9}{3k - 12} $ Now the expressions have the same denominator we can simply subtract the numerators: $a = \dfrac{-5k + 20 - (3k - 9) }{3k - 12} $ Distribute the negative sign: $a = \dfrac{-5k + 20 - 3k + 9}{3k - 12}$ $a = \dfrac{-8k + 29}{3k - 12}$